Mirror Mirror on the Wall

by Nicholas Mee on November 1, 2012

When Peter Higgs thought up the ideas behind the particle that we now know as the Higgs boson his aim was to find a way to bring together two of the fundamental forces of nature, known as the electromagnetic and weak forces. Following the success of his ideas,  we now know that these two forces are really just two aspects of a single electroweak force. The critical insight that Higgs provided was to show how the symmetry between the two forces could be hidden from us, or in physicists’ language how the symmetry could be broken.

The Viewer of Beautiful Forms

One of my main aims when writing my book Higgs Force was to explain what physicists mean when they say that a symmetry is broken. But before tackling symmetry breaking it was necessary to describe symmetry itself. The device that I chose for this purpose was the kaleidoscope, which was invented by the eminent Scottish scientist David Brewster in the early years of the 19th century. Brewster named his toy the “kaleidoscope” by combining three Greek words: “kalos” meaning beautiful, “eidos” meaning shape or form and “scopos” meaning viewer – the viewer of beautiful forms. As is well known, kaleidoscopes use collections of mirrors to produce symmetrical patterns. Mathematicians such as the great 20th century geometer Donald Coxeter have developed the kaleidoscope as a model for producing an abstract and completely general theory of symmetrical objects that could even be applied in higher dimensions.

Higgs Force in Colour

The new edition of Higgs Force contains colour plates showing various kaleidoscopic images that were included in the book to illustrate the discussion of symmetry. (The new Kindle and iTunes editions contain colour illustrations throughout.) The kaleidoscopic images are actually frames that were taken from animations that I produced using various raytracing programs. Some of these animations are shown here.

It’s All Done With Mirrors

The animation shown above was produced in a virtual kaleidoscope containing two mirrors. It has the same symmetry as a regular hexagon, so the images look similar to snowflakes.

I have left a space between the animations so that they are not too hypnotic.

 

 

 

 

 

 

 

 

The animation shown above was produced in a virtual kaleidoscope formed of four triangular mirrors. It shows a honeycomb of hexagonal prisms. (Mathematicians use the term ‘honeycomb’ to describe any collection of polyhedra that are stacked together to fill space without leaving any gaps. This particular kaleidoscopic image was not included in Higgs Force.)

 

 

 

 

 

 

 

 

The animation shown above was also produced in a virtual kaleidoscope formed of four triangular mirrors. It shows a honeycomb of truncated octahedra.

 

 

 

 

 

 

 

 

 

The animation shown above was also produced in a virtual kaleidoscope formed of four triangular mirrors. It shows a honeycomb of octahedra and cuboctahedra. A frame from this animation was used as the cover image for the first edition of Higgs Force.

More Information

An explanation of kaleidoscopes that I wrote for the SCIENAR project that includes high resolution versions of the animations:
http://www.virtualimage.co.uk/SCIENAR/html/kaleidoscopes.html

Prof. H.S.M. Coxeter who developed the mathematical theory of kaleidoscopes in higher dimensions:
http://en.wikipedia.org/wiki/Harold_Scott_MacDonald_Coxeter

The following link goes to a web page showing some of the Symbolic Sculpture animations that I produced with the sculptor John Robinson.
http://www.virtualimage.co.uk/SCIENAR/html/symbolic_sculpture.html

 

{ 2 comments… read them below or add one }

eswari.ch November 23, 2012 at 8:37 am

Sir, this is very interesting work that you have done which made me very much inspired to do so much scientific works.

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Shyamal Chakraborty November 28, 2012 at 5:31 am

Sir,
Please keep up your good work. I keenly await your posts. What I like particularly — is that while discussing the science you don’t get bogged down / or digress into particularities; and this is not an easy task.

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